Literature suggests that in order to perform valid inference on bandit data using traditional inferential methods it is necessary to guarantee that the bandit algorithm explores sufficiently. For example, existing estimators proposed in the adaptive setting, such as the BOLS [1]} and the AW-AIPW [2]}, are based on CLTs with conditions that implicitly impose constraints on the actions' sampling probabilities of the bandit algorithm (see Definition 1 in [1]} and Assumptions 1-3 in [2]}). These include avoiding action selection probabilities below certain thresholds (i.e, probability clipping) and/or consideration on the rate of convergence of these probabilities (see also Supplementary material C3).
In addition, other works [5]} also discuss how greater exploration with probability clipping may solve the problem of reduced power of a statistical tests in adaptively-collected data. Such property is supported by Figure REF , where the statistical power of the AW-AIPW-based Z-test is shown to improve by increasing the clipping threshold.
